Question

in a right angled triangle,if each acute angle is 45°,then the side opposite to 45° is 1/√2 times the hypotenuse

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Answer 1

Answer:

Let, in a right angled triangle ABC, right angled at B and Hypotenuse AC

<A = <C = 45°

Therefore AB = BC ( sides opposite to equal Angels are equal)

By pythagoras theorem

AB^2 + BC^2 = AC^2

AB^2 + AB^2 = AC^2 [BC =AB]

2 × AB^2 = AC^2

AB^2 = 1/2 × AC^2

AB = 1/√2 AC^2

or AB = BC = 1/√2 AC^2